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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}\,dx = } $
  • A
    $\frac{\pi }{2}$
  • B
    $\frac{\pi }{4}$
  • C
    $\frac{\pi }{6}$
  • ✓
    $\frac{\pi }{8}$
✓

Answer

Correct option: D.
$\frac{\pi }{8}$
d
(d) Put ${\sin ^2}x = t \Rightarrow dt = 2\sin x\cos x\,dx$

Now $\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}dx = \frac{1}{2}\int_0^1 {\frac{1}{{1 + {t^2}}}dt = \frac{1}{2}[{{\tan }^{ - 1}}t]_0^1 = \frac{\pi }{8}} } $.

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